How much higher is the true APR than the nominal interest rate once fees are amortized into the loan?
This tool is for: Borrowers comparing loan offers from different lenders · Anyone evaluating a quoted rate that comes with points or origination fees · People who want to understand why APR is legally required alongside the interest rate
- The monthly payment implied by the nominal interest rate
- The implied APR when fees are amortized into the loan
- The spread between the APR and the nominal rate — the true hidden cost of fees
Formulas Used
Fixed-Rate Monthly Payment
M = P × [r(1+r)^n] / [(1+r)^n − 1]
Where: M = Monthly principal + interest payment (USD), P = Loan principal (USD), r = Monthly interest rate (decimal), n = Total payments (months)
Source: Standard amortization — CFPB consumer guidance ✓ Verified
APR Implied by Net Disbursement
(P − fees) = M × [1 − (1 + APR/12)^−n] / (APR/12), solved iteratively for APR
Where: P − fees = Net amount disbursed to the borrower after subtracting upfront fees (USD), M = Monthly payment at the nominal interest rate (USD), APR = Annual Percentage Rate — the effective annual rate inclusive of fees (%), n = Total number of monthly payments (months)
Source: Regulation Z (Truth in Lending) — CFPB APR methodology ✓ Verified
Key Insight
A 0.25-point rate reduction bought with 1 discount point often does not pay for itself on loans held less than 6–7 years. The APR calculation is the fastest way to see whether paying points is worth it — compare the APR of the paid-points offer against the APR of the no-points offer over the same term.
Frequently Asked Questions
Why is APR always at least as high as the interest rate?
The nominal interest rate is charged on the full principal. The APR is the rate that, when applied to the amount you actually receive (principal minus upfront fees), reproduces the same monthly payment stream. Because the denominator shrinks (you received less cash than the face principal) while the payments stay the same, the effective annual rate must be higher. APR equals the nominal rate only when upfront fees are zero.
Why does a shorter term make the APR spread larger?
Fees are amortized across the payments. A 60-month loan spreads fees over 60 payments; a 360-month mortgage spreads them over 360. The shorter term concentrates each fee dollar over fewer months, raising its effective yearly rate impact. This is why a $500 fee on a 5-year personal loan can add nearly a full point to the APR, while the same $500 fee on a 30-year mortgage barely moves it.
Does paying discount points lower my APR?
Paying discount points lowers the nominal rate but counts as an upfront fee in the APR computation. The net effect can go either way. If the rate reduction is large enough that the present value of the lifetime monthly savings exceeds the point cost, APR falls. If you sell, refinance, or pay off early before that break-even, APR rises. Use this calculator twice — once with points (lower rate, higher fee) and once without — to compare APR side by side.
About This Calculator
Sources:
- Consumer Financial Protection Bureau — What is the difference between a mortgage interest rate and an APR? — Official CFPB explanation of the distinction between nominal interest rate and APR, including which fees enter the APR computation
- Regulation Z (Truth in Lending Act) — §1026.22 APR Computation — Federal regulatory methodology that lenders must follow when computing and disclosing APR
Limitations:
- Assumes simple upfront-fee model — does not separate prepaid finance charges from non-finance charges
- APR computed via bisection; lender-disclosed APR may differ by a few basis points due to rounding and fee classification
- Excludes third-party fees that legally sit outside the APR (title, appraisal, government recording)
- Does not handle variable-rate loans, interest-only periods, or balloon payments
- For mortgages, the APR does not include PMI, property taxes, insurance, or HOA
When to consult a professional: Before closing on any mortgage or loan above $50,000, or when the lender's disclosed APR differs by more than 0.125 percentage points from this estimate
This calculator estimates the APR implied by the simplest Truth-in-Lending model — fees reduce the net disbursed amount while monthly payments remain driven by the nominal rate. Regulation Z permits several APR computation methods; a specific lender's disclosed APR may differ slightly due to fee classification, rounding conventions, or treatment of prepaid finance charges. Use the result for comparison shopping, not as a substitute for the lender's official TILA disclosure.